A first-principles calculation with Quantum ESPRESSO
The following is a very basic calculation of Z2 invariants using Quantum ESPRESSO for Bismuth. The complete example (including input files) can be found on GitHub.
#!/usr/bin/env python
import os
import shutil
import subprocess
import xml.etree.ElementTree as ET
import matplotlib.pyplot as plt
import z2pack
# Edit the paths to your Quantum Espresso and Wannier90 here
qedir = "/home/greschd/software/espresso-5.4.0/bin/"
wandir = "/home/greschd/software/wannier90-1.2"
# Commands to run pw, pw2wannier90, wannier90
mpirun = "mpirun -np 4 "
pwcmd = mpirun + qedir + "/pw.x "
pw2wancmd = mpirun + qedir + "/pw2wannier90.x "
wancmd = wandir + "/wannier90.x"
z2cmd = (
wancmd
+ " bi -pp;"
+ pwcmd
+ "< bi.nscf.in >& pw.log;"
+ pw2wancmd
+ "< bi.pw2wan.in >& pw2wan.log;"
)
# creating the results folder, running the SCF calculation if needed
if not os.path.exists("./plots"):
os.mkdir("./plots")
if not os.path.exists("./results"):
os.mkdir("./results")
if not os.path.exists("./scf"):
os.makedirs("./scf")
print("Running the scf calculation")
shutil.copyfile("input/bi.scf.in", "scf/bi.scf.in")
out = subprocess.call(pwcmd + " < bi.scf.in > scf.out", shell=True, cwd="./scf")
if out != 0:
raise RuntimeError(
"Error in SCF call. Inspect scf folder for details, and delete it to re-run the SCF calculation."
)
# Copying the lattice parameters from bi.save/data-file.xml into bi.win
cell = ET.parse("scf/bi.save/data-file.xml").find("CELL").find("DIRECT_LATTICE_VECTORS")
unit = cell[0].attrib["UNITS"]
lattice = "\n ".join([line.text.strip("\n ") for line in cell[1:]])
with open("input/tpl_bi.win") as f:
tpl_bi_win = f.read()
with open("input/bi.win", "w") as f:
f.write(tpl_bi_win.format(unit=unit, lattice=lattice))
# Creating the System. Note that the SCF charge file does not need to be
# copied, but instead can be referenced in the .files file.
# The k-points input is appended to the .in file
input_files = ["input/" + name for name in ["bi.nscf.in", "bi.pw2wan.in", "bi.win"]]
system = z2pack.fp.System(
input_files=input_files,
kpt_fct=[z2pack.fp.kpoint.qe, z2pack.fp.kpoint.wannier90],
kpt_path=["bi.nscf.in", "bi.win"],
command=z2cmd,
executable="/bin/bash",
mmn_path="bi.mmn",
)
# Run the WCC calculations
result_0 = z2pack.surface.run(
system=system,
surface=lambda s, t: [0, s / 2, t],
save_file="./results/res_0.json",
load=True,
)
result_1 = z2pack.surface.run(
system=system,
surface=lambda s, t: [0.5, s / 2, t],
save_file="./results/res_1.json",
load=True,
)
# Combining the two plots
fig, ax = plt.subplots(1, 2, sharey=True, figsize=(9, 5))
z2pack.plot.wcc(result_0, axis=ax[0])
z2pack.plot.wcc(result_1, axis=ax[1])
plt.savefig("plots/plot.pdf", bbox_inches="tight")
print(f"Z2 topological invariant at kx = 0: {z2pack.invariant.z2(result_0)}")
print(f"Z2 topological invariant at kx = 0.5: {z2pack.invariant.z2(result_1)}")